Short Resolution refutations of Ref(φ) yield satisfying assignments for φ in polynomial time via a PV1-formalizable construction, and the Proof Analysis Problem is NP-complete for Extended Frege.
Using the Groebner basis algo- rithm to find proofs of unsatisfiability
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Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.
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The Proof Analysis Problem
Short Resolution refutations of Ref(φ) yield satisfying assignments for φ in polynomial time via a PV1-formalizable construction, and the Proof Analysis Problem is NP-complete for Extended Frege.
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Average-Case Hardness of Binary-Encoded Clique in Proof and Communication Complexity
Exponential lower bounds for cutting planes and Res(⊕) on binary clique formulas for random dense graphs, with polynomial randomized communication complexity for falsified clause finding.